Design of Experiments for Generalized Linear Models
Generalized Linear Models (GLMs) allow many statistical analyses to be extended to important statistical distributions other than the Normal distribution. While numerous books exist on how to analyse data using a GLM, little information is available on how to collect the data that are to be analysed in this way.
This is the first book focusing specifically on the design of experiments for GLMs. Much of the research literature on this topic is at a high mathematical level, and without any information on computation. This book explains the motivation behind various techniques, reduces the difficulty of the mathematics, or moves it to one side if it cannot be avoided, and gives examples of how to write and run computer programs using R.
- The generalisation of the linear model to GLMs
- Background mathematics, and the use of constrained optimisation in R
- Coverage of the theory behind the optimality of a design
- Individual chapters on designs for data that have Binomial or Poisson distributions
- Bayesian experimental design
- An online resource contains R programs used in the book
This book is aimed at readers who have done elementary differentiation and understand minimal matrix algebra, and have familiarity with R. It equips professional statisticians to read the research literature. Nonstatisticians will be able to design their own experiments by following the examples and using the programs provided.
Generalized Linear Models
The Theory Underlying Design
The Binomial Distribution
The Poisson Distribution
Several Other Distributions
Bayesian experimental design
"Dr Russell has produced an accessible and informative text that provides useful methodology for applied researchers and practitioners, and a good introduction for postgraduate students wishing to start researching in the area. Design of experiments is fundamental to the scientific method but, when non-normal data is anticipated, too often either little thought is given to the design, or inappropriate designs tailored to linear models are applied. This book provides the background and methods, including R code, required to start designing better experiments in such situations. The coverage ranges from relatively simple, single factor experiments to multi-factor studies and Bayesian designs using recent research results, making is a valuable addition to many different bookshelves."
—Professor David Woods, University of Southampton
"…this is the first book written specifically on the design of experiments for generalized linear models (GLMs). Code (in R) for handling all the calculations described is available online…This text is helpful as a careful overview of both linear models and GLMs, with some articulation of design implications."
-John H. Maindonald, ISR 2019
"This book fills an important gap in the existing literature on the Design of Experiments. Existing books cover extensively the general linear model, describing topics of Generalized Linear Models (GLMs) for the Design of Experiments (DoE) in only a chapter or so. This book consists of seven chapters. A dedicated website, mainly containing R code for the implementation of the described methods, is maintained by the author (https://doeforglm.com). Known errata can also be found there... particularly useful aspect of the book is the exposition of small sample size effects in the modelling process and ways to cope with this in practice. Small sample sizes are encountered very often in practice in the Design of Experiments, both in the industrial and the agricultural sectors. Similarly, in Chapter 5, the Poisson distribution case is presented, including how to model such data, and how to find relevant D-optimal designs. Useful numerical examples are also given... The book should be particularly useful for researchers working in industry, interested in designing their own experiments when the outcome variable can be modelled by the GLM family of distributions. It could also be very useful for both theoretical and applied researchers in academia, interested in developing skills (each for their own reasons) in this particular area that finds useful applications in different fields of applied research such as -omics and Big Data problems."
- Christos T. Nakas, University of Thessaly, Appeared in ISCB News, January 2020